Suppose the elements X and Y combine to form two compounds XY₂ and X₃Y₂ When 0.1 mole of XY₂  weighs 10 g and 0.05 mole of X₃Y₂ weighs 9 g, the atomic weights of X and Y are

Let atomic weight of element  X is x and that of element Y is y.
For $X{Y}_2,n=\frac{w}{Mol.wt.}$
$0.1=\frac{10}{x+2y}\Rightarrow x+2y=\frac{10}{0.1}=\mathrm{100...............}\left(i\right)$
For $X_3{Y}_2,n=\frac{w}{Mol.wt.}$
$0.5=\frac{9}{3x+2y}\Rightarrow 3x+2y=\frac{9}{0.05}=\mathrm{180...............}\left(ii\right)$
On solving equations (i) and (ii), we get 
x = 40
$40+2y=100\Rightarrow 2y=60\Rightarrow y=30$